CBSE Class 12-science Answered

pls solve

Asked by sdmbotch1123 | 18 Jan, 2023, 11:01: PM

Expert Answer

Let

begin mathsize 14px style b with rightwards arrow on top space equals space alpha space i with hat on top space plus space beta space j with hat on top space plus space gamma space k with hat on top space end style

begin mathsize 14px style a with rightwards arrow on top space cross times space b with rightwards arrow on top space equals space open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell cell k with hat on top end cell row 1 1 1 row alpha beta gamma end table close vertical bar space equals space open parentheses gamma minus beta close parentheses i with hat on top space plus open parentheses alpha minus gamma close parentheses j with hat on top space plus space open parentheses beta minus alpha close parentheses k with hat on top end style

................................. (1)

We are given that

begin mathsize 14px style a with rightwards arrow on top space cross times b with rightwards arrow on top space equals space j with hat on top space minus space k with hat on top end style

....................................... (2)

By comparing eqn.(1) and eqn.(2) , we get

β = γ .............................. (3)

α - γ = 1 or γ = α - 1

β - α = -1 or β = α - 1

begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top space equals space open parentheses space i with hat on top space plus space j with hat on top space plus space k with hat on top close parentheses space times space open parentheses alpha space i with hat on top space plus beta space j with hat on top space plus gamma space k with hat on top close parentheses space equals space alpha plus beta plus gamma end style

we are given that

begin mathsize 14px style a with rightwards arrow on top times b with rightwards arrow on top space equals space 3 end style

hence we get

begin mathsize 14px style alpha space plus space beta space plus space gamma space equals space 3 end style

α + ( α -1 ) + ( α -1 ) = 3 α -2 = 3

α = 5/3 ; β = α - 1 = (5/3) - 1 = (2/3) ; γ = β = (2/3)

Hence

begin mathsize 14px style c with rightwards arrow on top space equals space 1 third open parentheses 5 space i with hat on top space plus space 2 j with hat on top space plus space 2 k with hat on top close parentheses end style

begin mathsize 14px style open vertical bar c with rightwards arrow on top close vertical bar space equals space 1 third open parentheses square root of 25 plus 4 plus 4 end root close parentheses space equals space square root of 33 over 9 end root space equals space square root of 11 over 3 end root end style

Answered by Thiyagarajan K | 19 Jan, 2023, 12:17: AM

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